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The pseudo-4D Doyle-Fuller-Newman (DFN) model enables predictive simulation of lithium-ion batteries with three-dimensional electrode architectures and particle-scale diffusion, extending the standard pseudo-2D (P2D) formulation to fully…
We develop a full-wave electromagnetic (EM) theory for calculating the multipole decomposition in two-dimensional (2-D) structures consisting of isolated, arbitrarily shaped, inhomogeneous, anisotropic cylinders or a collection of such. To…
Thin films are gaining ground in photonics and optoelectronics, promising improvements in their efficiency and functionality as well as decreased material usage as compared to bulk technologies. However, proliferation of thin films would…
The electroosmotic transfer (ratio of velocity of liquid to electric current density) and conductivity of disperse system were calculated as functions of volume fraction of disperse particles. The considered model of electric double layer…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The use of eco-friendly materials for the environment has been addressed as a critical issue in the development of systems for renewable energy applications. In this regard, the investigation of organic photovoltaic (OPV) molecules for the…
The observed convective flows on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock-Leighton (BL) process to generate large-scale polar fields from sunspots fields. In most surface flux transport (SFT) and…
A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
Modeling the charge-generation process is highly important to understand device physics and optimize power conversion efficiency of bulk-heterojunction (BHJ) organic solar cells (OSCs). Free carriers are generated by both ultrafast exciton…
Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically…
A multi-timescale hybrid model is proposed to study microscopically the degraded performance of electronic devices, covering three individual stages of radiation effects studies, including ultrafast displacement cascade, intermediate defect…
The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. In this work, we propose a macroscopic mathematical…
Dye-sensitized solar cells (DSC), built upon organic/inorganic hybrid materials, are promising third generation solar cells, which attract wide attentions due to their low-cost, flexibility and environment-friendly properties. We review…
The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described…
Fuel cells, batteries, thermochemical and other energy conversion devices involve the transport of a number of (electro-)chemical species through distinct materials so that they can meet and react at specified multi-material interfaces.…
We present a pipeline to study the device performance of organic solar cells in silico. We introduce a mathematical model that includes the dynamics of excitons as well as their dissociation at bulk heterojunctions within the nanomorphology…
Babcock-Leighton type solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…